There is a passage in Peter van Inwagen's "Existence, Ontological Commitment, and Fictional Entities," (in Existence: Essays in Ontology, CUP, 2014, p. 98, emphasis added), in which he expresses his incomprehension of what the Meinongian means by 'has being' and 'lacks being':
… the Meinongian must mean something different by 'has being' and 'lacks being' from what I mean by these phrases. But what does he mean by them? I do not know. I say 'x has being' means '~(y) ~y = x'; the Meinongian denies this. Apparently, he takes 'has being' to be a primitive, an indefinable term, whereas I think that 'has being' can be defined in terms of 'all' and 'not'. (And I take definability in terms of 'all' and 'not' to be important, because I am sure that the Meinongian means exactly what I do by 'all' and 'not' -- and thus he understands what I mean by 'has being' and is therefore an authority on the question whether he and I mean the same.) And there the matter must rest. The Meinongian believes that 'has being' has a meaning that cannot be explained in terms of unrestricted universal quantification and negation.
Before I begin, let me say that I don't think van Inwagen is feigning incomprehension as some philosophers are wont to do: I believe he really has no idea what 'has being' and cognate expressions could mean if they don't mean what he thinks they mean.
No one articulates and defends the thin theory of existence/being better than Peter van Inwagen who is arguably 'king' of the thin theorists. The essence of the thin theory is that
1. x exists =df ~(y)~(y=x).
Driving the tilde though the right-hand expression, left to right, yields the logically equivalent
1*. x exists =df (∃y)(y = x)
which may be easier for you to wrap your head around. In something closer to English
1**. x exists =df x is identical to something.
The thin theory is 'thin' because it reduces existence to a purely logical notion definable in terms of the purely logical notions of unrestricted universal quantification, negation, and identity. What is existence? On the thin theory existence is just identity-with-something. (Not some one thing, of course, but something or other.) Characteristically Meinongian, however, is the thesis of Aussersein which could be put as follows:
M. Some items have no being.
Now suppose two things that van Inwagen supposes. Suppose that (i) there is exactly one sense of 'exists'/'is' and that (ii) this one sense is supplied in its entirety by (1) and its equivalents. Then (M) in conjunction with the two suppositions entails
C. Some items are not identical to anything.
But (C) is self-contradictory since it implies that some item is such that it is not identical to itself, i.e. '(∃x)~(x = x).'
Here we have the reason for van Inwagen's sincere incomprehension of what the Meinongian means by 'has being.' He cannot understand it because it seems to him to be self-contradictory. But it is important to note that (M) by itself is not logically contradictory. It is contradictory only in conjunction with van Inwagen's conviction that 'x has being' means '~(y) ~(y = x).'
In other words, if you ASSUME the thin theory, then the characteristic Meinongian thesis (M) issues in a logical contradiction. But why assume the thin theory? Are we rationally obliged to accept it?
I don't accept the thin theory, but I am not a Meinongian either. 'Thin or Meinongian' is a false alternative by my lights. I am not a Meinongian because I do not believe that existence is a classificatory principle that partitions a logically prior domain of ontologically neutral items into the existing items and the nonexisting items. I hold that everything exists, which, by obversion, implies that nothing does not exist. So I reject (M).
I reject the thin theory not because some things don't exist, but because there is more to the existence of what exists than identity-with-something. And what more is that? To put it bluntly: the more is the sheer extralogical and extralinguistic existence of the thing, its being there (in a non-locative sense of course). The 'more' is its not being nothing. (If you protest that to not be nothing is just to be something, where 'something' is just a bit of logical syntax, then I will explain that there are two senses of 'nothing' that need distinguishing.) Things exist, and they exist beyond language and logic.
Can I argue for this? It is not clear that one needs to argue the point since it is, to me at least, self-evident. But I can argue for it anyway.
If for x to exist is (identically) for x to be identical to some y, this leaves open the question: does y exist or not? You will say that y exists. (If you say that y does not exist, then you break the link between existence and identity-with-something.) So you say that y exists. But then your thin theory amounts to saying that the existence of x reduces to its identity with something that exists. My response will be that you have moved in an explanatory circle, one whose diameter is embarrassingly short. Your task was to explain what it is for something to exist, and you answer by saying that to exist is to be identical to something that exists. This response is no good, however, since it leaves unexplained what it is for something to exist! You have helped yourself to the very thing you need to explain.
It is the extralogical and extralinguistic existence of things that grounds our ability to quantify over them. Given that things exist, and that everything exists, we have no need for an existence predicate: we can rid ourselves of the existence predicate 'E' by defining 'Ex' in terms of '(∃y)(y = x).' But note that the definiens contains nothing but logical syntax. What this means is that one is presupposing the extralogical existence of items in the domain of quantification. You can rid yourself of the existence predicate if you like, but you cannot thereby rid yourself of the first-level existence of the items over which you are quantifying.
Here is another way of seeing the point. Russell held that existence is a propositional function's being sometimes true. Let the propositional function be (what is expressed by) 'x is a dog.' That function is sometimes true (in Russell's idiosyncratic phraseology) if the free variable 'x' has a substituend that turns the propositional function or open sentence into a true closed sentence. So consider 'Fido,' the name of an existing dog and 'Cerberus.' How do I know that substituting 'Fido' for 'x' results in a true sentence while substituting 'Cerberus' does not? Obviously, I must have recourse to a more fundamental notion of existence than the one that Russell defines. I must know that Fido exists while Cerberus does not. Clearly, existence in the fundamental sense is the existence that belongs to individuals, and not existence as a propositional function's being sometimes true.
Now if you understand the above, then you will be able to understand why, in van Inwagen's words, "The Meinongian believes that 'has being' has a meaning that cannot be explained in terms of unrestricted universal quantification and negation." The thin theory entails that there is no difference in reality between x and existing x. But for Meinong there is a difference: it is the difference between Sosein and Sein. While I don't think that there can be a Sosein that floats free of Sein. I maintain that there is a distinction in reality between a thing (nature, essence, Sosein, suchness) and existence.
If van Inwagen thinks that he has shown that Meinong's doctrine entails a formal-logical contradiction, he is fooling himself. Despite his fancy footwork and technical rigmarole, all van Inwagen succeeds in doing is begging the question against Meinong.